Explain why all variables but one should be controlled in a well designed experiment.

 All variables should be controlled except the one being tested because it would allow to ascertain the researcher that the results is truly an effect of that one and tested variable. This variable is called the independent variable. It is what is being changed and manipulated in a research to effect a change to the dependent variable which is the variable being studied.

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If the heat engine is a perfect carnot cycle engine, thenefficiency = (t2-t1)/t2   where t1=temperature of cold reservoir ( ° k) = 135            t2=temperature of hot reservoir ( ° k)   = 325thereforeefficiency = (t2-t1)/t2 = (325-135)/325 = 0.5846 = 58%  note: this is the theoretical maximum efficiency of a perfect heat engine.   real-life engines do not achieve this value.